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Popular >

derivative of arctan(sin(3x))

Solution

\frac{d}{d x} (arctan (sin (3 x)))

Solution

\frac{3 cos ( 3 x )}{sin ^{2} ( 3 x ) + 1}

Solution steps

\frac{d}{d x} (arctan (sin (3 x)))

Apply the chain rule:

\frac{1}{( sin ( 3 x ) ) ^{2} + 1} \frac{d}{d x} (sin (3 x))

= \frac{1}{( sin ( 3 x ) ) ^{2} + 1} \frac{d}{d x} (sin (3 x))

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= \frac{1}{( sin ( 3 x ) ) ^{2} + 1} cos (3 x) \cdot 3

Simplify

\frac{1}{sin ^{2} ( 3 x ) + 1} cos (3 x) \cdot 3 : \frac{3 cos ( 3 x )}{sin ^{2} ( 3 x ) + 1}

= \frac{3 cos ( 3 x )}{sin ^{2} ( 3 x ) + 1}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arctan(sin(3x)) ?
The derivative of arctan(sin(3x)) is (3cos(3x))/(sin^2(3x)+1)
What is the first derivative of arctan(sin(3x)) ?
The first derivative of arctan(sin(3x)) is (3cos(3x))/(sin^2(3x)+1)